Your big challenge in wanting to sail on the Potomac beyond draft issues is finding a slip. They are notoriously difficult to get in my experience. If you're on base with slip access (Quantico) you might have an easier time. But usually the Potomac marinas that support sailboats have waiting lists 1-2 years long.
I had an O'Day 22 on the Potomac. Bought it as a turnkey boat. It was at Washington Sailing Marina south of Reagan Airport and my experience has been borne out that the only way into the marina short of a long wait is to literally buy a boat already there. They'll transfer the slip to you if the seller agrees as part of the transaction. I see ads fairly regularly for boats at WSM that include slip transfers.
Draft is an issue. To maintain access, a draw of 2 1/2 feet or less is ideal. Deeper drafts can work but you'll have to pay close attention to your charts and stick to the channels. Given the narrowness of the Potomac in many places this can severely limit your sailing options. Even with my O'Day's sub 2-foot draw I still ran her aground once.
Despite wanting to start out small on the Potomac, my wife quickly wanted to upgrade the next season to something that didn't require us having to tack every 10 minutes as well and play dodge the powerboat in crossing two shipping channels. Now we're on the Bay with a lot more open space.
You don't necessarily need to take the courses to get the big boat experience. Get to know local sailors and groups for various boats and you'll have no problem finding rides on other people's boats.
In terms of boat type, that is up to you. What can you handle cost and rig-wise? Given my wife only likes to assist in pulling the jib sheets, I single-hand the boat most of the time so that drove a lot of my decision making. Like your spouse, mine wanted a galley, a head, some space down below. To get that you'll need to be looking at boats usually no smaller than 26 feet to get at least six feet of headroom down below. 27-30 feet is the usual "sweet spot" for first boats in terms of affordability, ongoing costs, sail handling, docility and so on.
But with the Potomac, you'll have to pay very close attention to the keel setup to get a boat in that size with low draft. Most are shoal draft keels or swing keels.
Consider the Chesapeake Bay. Seriously. Middle Bay between Pax River and Annapolis is within an hour's drive and there are lots of options for marinas and boats. And with the exception of the marina approaches, you won't be constrained heavily by draft in most cases. My Catalina 27 draws 4 feet. Can't get into some places say a shoal draft keel can but shallow enough for most of the Bay and more access than boats that draw 6 feet. And lots of wonderful places you can daysail or overnight to and enjoy the dinner/cocktail thing.
SV South Paw
2000 Hunter 340
South River, MD